There are two kinds of planets in the solar system: the Terrestrial planets (Mercury, Venus, Earth, Mars), and the Jovian planets (Jupiter, Saturn, Uranus, Neptune). While the Jovian planets have a total observed number of moons of close to 90, the Terrestrial planets have only 3 (the Moon, and two small moons around Mars). This huge difference is linked to the formation of the solar system.

The solar system formed out of a giant, swirling cloud of gas, which collapsed under its own gravity. During this collapse, the gas heated up, started to rotate faster in an orderly manner. This led to the formation of what's called the protoplanetery disk: a disk of hot rotating gas, with the mass concentrated at the centre. This central concentration became the Sun, and planets formed out of the remaining disk.

The gas in the protoplanetery disk could not collapse by itself to form the planets. It needed some 'seeds', which gravity could pull together. The variety in the planets is linked to the kind of 'seeds' that were available in the different parts of the protoplanetary disk. Near the Sun, the temperature was so high that all the material was gas and could not form planets. A little farther from the Sun, there were metal flakes and small pieces of rock. These flakes stuck together when they collided, forming planetesimals. These planetesimals grew quickly in size, until they became so big that collisions started to break them apart. Only the largest survived that to become the Terrestrial planets.

Outside of the orbit of Mars, the temperature was low enough, that there were not only flakes of metal and chunks of rock, but also many small pieces of ice. There was therefore more 'seeds' to form planets of. This caused the planetesimals to grow quickly, and to become large enough that their gravity could capture hydrogen and helium which was very abundant in the protoplanetery disk. The protoplanets captured so much gas, that they became 'tiny solar systems'. By that I mean that the same heating, spinning and flattening happened, resulting in the formation of many icy satellites around the Jovian planets. This can account for the majority of the moons around Jovian planets. They have however some other moons that are leftover planetesimals that the planets captured.

This in fact is probably the origin of the two moons around Mars: they were two small protoplanets that the gravity of Mars pulled in its orbit. As for our Moon, the story is believed to be different. It is assumed that the Moon formed from the collision of a large planetesimal with the Earth. This collision would have ejected a lot of material into Earth's orbit that contracted to form our satellite, the Moon.

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